Question

x+y-1=0 prove that x^3+y^3+3xy=1

Answer 1

Answer:

Given:

• x + y - 1 = 0.

Find:

• Prove that x³ + y³ + 3xy = 1.

Calculation:

⇒ (x + y) = 1

⇒ x³ + y³ = (x + y) (x² + y² - xy)

⇒ x³ + y³ = (x + y) [(x + y)² - 2xy - xy)

⇒ x ³+ y³ = (x + y) [(x + y)² - 3xy]

Adding, (x + y) = 1, we get:

⇒ x³ + y³ = [1] [(1)² - 3xy]

⇒ x³ + y³ = 1 - 3xy

⇒ x³ + y³ + 3xy = 1

HENCE PROVED!!!